Question: Simplify the following expression: $ q = \dfrac{t + 5}{4t - 4} - \dfrac{-8}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{t + 5}{4t - 4} \times \dfrac{3}{3} = \dfrac{3t + 15}{12t - 12} $ Multiply the second expression by $\dfrac{4t - 4}{4t - 4}$ $ \dfrac{-8}{3} \times \dfrac{4t - 4}{4t - 4} = \dfrac{-32t + 32}{12t - 12} $ Therefore $ q = \dfrac{3t + 15}{12t - 12} - \dfrac{-32t + 32}{12t - 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{3t + 15 - (-32t + 32) }{12t - 12} $ Distribute the negative sign: $q = \dfrac{3t + 15 + 32t - 32}{12t - 12}$ $q = \dfrac{35t - 17}{12t - 12}$